Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths

被引：0
作者：
Laurent Denis
Mingshang Hu
Shige Peng
机构：
[1] Université d’Evry-Val-d’Essonne,Département de Mathématiques, Equipe “Analyse et Probabilités”
[2] Shandong University,School of Mathematics
[3] Fudan University,School of Mathematics
来源：
Potential Analysis | 2011年 / 34卷
关键词：
Capacity; Sublinear expectation; -expectation; -Brownian motion; Dynamic programming principle; 60G05; 60G17; 31A15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we give some basic and important properties of several typical Banach spaces of functions of G-Brownian motion paths induced by a sublinear expectation—G-expectation. Many results can be also applied to more general situations. A generalized version of Kolmogorov’s criterion for continuous modification of a stochastic process is also obtained. The results can be applied in continuous time dynamic and coherent risk measures in finance, in particular for path-dependence risky positions under situations of volatility model uncertainty.
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页码：139 / 161
页数：22
相关论文
共 36 条
[1]  
Artzner P(1999)Coherent measures of risk Math. Financ. 9 203-228
[2]  
Delbaen F(1995)Pricing and hedging derivative securities in markets with uncertain volatilities Appl. Math. Financ. 2 73-88
[3]  
Eber J-M(2002)Ambiguity, risk and asset returns in continuous time Econometrica 70 1403-1443
[4]  
Heath D(1955)Theory of capacities Ann. Inst. Fourier 5 131-295
[5]  
Avellaneda M(1992)User’s guide to viscosity solutions of second order partial differential equations Bull. Am. Math. Soc. 27 1-67
[6]  
Levy A(1992)Representing martingale measures when asset prices are continuous and bounded Math. Financ. 2 107-130
[7]  
Paras A(2009)Representation of the penalty term of dynamic concave utilities Finance Stoch. 16 827-852
[8]  
Chen Z(2006)A theorical framework for the pricing of continent claims in the presence of model uncertainty Ann. Appl. Probab. 7 1-71
[9]  
Epstein L(1997)Backward stochastic differential equation in finance Math. Financ. 39–4 875-908
[10]  
Choquet G(1989)Espaces de Sobolev Gaussiens Ann. Inst. Fourier 6 429-447
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